196 ELEMENTARY LESSONS ON [CHAP. iv. 



Hence the work done in passing from r to r will be 



On a similar assumption, the work done in passing from r^ 

 to r lt will be 



q ( ; ) , and that done from r 3 to r^ will be 



v ' i ' 'V* 



= ? ( - --- - J etc., giving us n equations, of which 

 the last will be the work done in passing from r to r n _ l 



Adding up all these portions of the work, the intermediate 

 values of r cancel out, and we get for the work done in pass- 

 ing from Q to P 



Next suppose Q to be an infinite distance from A. Here 

 r' = infinity, and -y- = o. In that case the equation 



becomes 



V = 2- 

 p r 



If instead of one quantity of electricity q, there were a 

 number of electrified particles having charges q' t q", q'" .... 



etc., at distances of r, r", r'" etc., respectively from 



P, then 



which was to be proved. 



239. Zero Potential. At a place infinitely distant 

 from all electrified bodies there would be no electric 

 forces and the potential would be zero. For purposes 

 of convenience it is, however, usual to consider the 

 potential of the earth for the time being as an arbitrary 



